Vivaldi does have a sync feature!
But I don't know if you're aware of that already, and FF/Chrome sync have something special in their Sync that Vivaldi doesn't.
EDIT: I want to add that I run the Snapshot versions of Vivaldi (currently 1.16.1211.3), and it could be that the Sync was introduced only in a Snapshot in December. So I have no idea if the sync can be found in the Stable releases as well. Anyways, it's under Tools/Settings/Sync tab if it's there, otherwise it isn't :)
I might not be the heaviest of the heavy users (figuratively speaking :), for example I have total of 3 Chrome extensions installed (uBlock origin, some exif viewer and Google translate), so I am not aware of things that may not have worked correctly.
I used to use Opera (first 12, then the Chrome version of Opera which I didn't like), and then switched to Vivaldi when I found out about it.